Question

A particle moves in a straight line along x-axis. Its position (x) varies with time (t) as x = 2t2 – 5t + 6, where all quantities are in SI units. Then Average velocity in first 3 s is 1 m/s Velocity at t = 3 s is 7 m/s Particle comes to rest at t=1s o Average acceleration in first 3 s is 4 m/s2​

Answer 1

Answer:

Option B is correct as the velocity at t=3 s is 7m/s

Answer 2

Given : A particle moves in a straight line along x-axis. Its position (x) varies with time (t) as x = 2t² – 5t + 6

To Find : Correct option:

Solution:

x = 2t² – 5t + 6

at t=0  x  =  6

at t = 3   x = 18 - 15 + 6  = 9

Hence Displacement in 3 secs = 9 - 6 = 3 m

Average velocity = 3/3 = 1 m/s

Average velocity in first 3 secs in 1 m/s  is correct

x = 2t² – 5t + 6

v= dx/dt  = 4t - 5

t = 3  =>  4(3) - 5 = 7

Hence Velocity at t = 3 is 7 m/s  is also correct

at rest velocity is zero

Hence 4t - 5 = 0

=> t = 5/4

Particle comes  to rest at 5/4 sec

Hence Particle comes  to rest at 1 sec is Incorrect

v =  4t - 5

at  t = 0    , v = - 5

at t = 3    v = 7

average acceleration = (7 - (-5))/3

= 12/3

= 4 m/s²

Hence Average acceleration is first 3 secs is 4m/s² is correct

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